Consider a project to supply Detroit with $20,000$ tons of machine screws annually for automobile production. You will need an initial $$3,400,000$ investment in threading equipment to get the project started; the project will last for $4$ years. The accounting department estimates that annual fixed costs will be $$800,000$ and that variable costs should be $$180$ per ton; accounting will depreciate the initial fixed asset investment straight$-$line to zero over the $4-$year project life. It also estimates a salvage value of $$620,000$ after dismantling costs. The marketing department estimates that the automakers will let the contract at a selling price of $$300$ per ton. The engineering department estimates you will need an initial net working capital investment of $$340,000.$ You require a return of $14$ percent and face a marginal tax rate of $23$ percent on this project. Suppose you$$re confident about your own projections, but you$$re a little unsure about Detroit$$s actual machine screw requirements.

a$.$

What is the sensitivity of the project OCF to changes in the quantity supplied? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

b$.$

What about the sensitivity of NPV to changes in quantity supplied? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$

c$.$

Given the sensitivity number you calculated, is there some minimum level of output below which you wouldn$$t want to operate? $($Do not round intermediate calculations and round your answer to $2$ decimal places, e$.$g$.,32\mathrm{.}16.)$